scholarly journals A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems

2011 ◽  
Vol 10 (6) ◽  
pp. 1791-1816 ◽  
Author(s):  
D. Motreanu ◽  
Donal O'Regan ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Critical Point ◽  
Multiple Solutions ◽  
Neumann Problems

Multiple Solutions for Nonlinear Neumann Problems with Asymmetric Reaction, via Morse Theory

2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Variational Methods ◽  
Neumann Problem ◽  
Morse Theory ◽  
Multiple Solutions ◽  
Smooth Solutions ◽  
Asymmetric Reaction ◽  
Neumann Problems ◽  
Nonlinear Neumann Problem ◽  
Asymmetric Behaviour ◽  
Nonlinear Neumann Problems

AbstractWe consider a nonlinear Neumann problem driven by the p-Laplacian and with a reaction which exhibits an asymmetric behaviour near +∞ and near −∞. Namely, it is (p − 1)- superlinear near +∞ (but need not satisfy the Ambrosetti-Rabinowitz condition) and it is (p − 1)-linear near −∞. Combining variational methods with Morse theory, we show that the problem has at least three nontrivial smooth solutions.

scholarly journals Multiple solutions for some Neumann problems in exterior domains

2006 ◽  
Vol 73 (3) ◽  
pp. 353-364 ◽  
Author(s):  
Tsing-San Hsu ◽  
Huei-Li Lin
Keyword(s):  
Neumann Problem ◽  
Multiple Solutions ◽  
The Other ◽  
Exterior Domains ◽  
Neumann Problems ◽  
The Neumann Problem

In this paper, we show that if q(x) satisfies suitable conditions, then the Neumann problem -Δu+u = q(x)ⅠuⅠp−2u in Ω has at least two solutions of which one is positive and the other changes sign.

Existence of multiple solutions with precise sign information for superlinear Neumann problems

2009 ◽  
Vol 188 (4) ◽  
pp. 679-719 ◽  
Author(s):  
Sergiu Aizicovici ◽  
Nikolaos S. Papageorgiou ◽  
Vasile Staicu
Keyword(s):  
Multiple Solutions ◽  
Neumann Problems

scholarly journals Multiple solutions for superlinear double phase Neumann problems

2021 ◽  
Vol 116 (1) ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rădulescu ◽  
Youpei Zhang
Keyword(s):  
Neumann Problem ◽  
Ground State ◽  
Multiple Solutions ◽  
Nehari Manifold ◽  
Ground State Solutions ◽  
Neumann Problems ◽  
Double Phase ◽  
The Nehari Manifold ◽  
Superlinear Reaction

AbstractWe study a double phase Neumann problem with a superlinear reaction which need not satisfy the Ambrosetti-Rabinowitz condition. Using the Nehari manifold method, we show that the problem has at least three nontrivial bounded ground state solutions, all with sign information (positive, negative and nodal).

Infinitely many solutions for non-homogeneous Neumann problems in Orlicz-Sobolev spaces

2018 ◽  
Vol 68 (4) ◽  
pp. 867-880
Author(s):  
Saeid Shokooh ◽  
Ghasem A. Afrouzi ◽  
John R. Graef
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Neumann Problem ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Neumann Problems

Abstract By using variational methods and critical point theory in an appropriate Orlicz-Sobolev setting, the authors establish the existence of infinitely many non-negative weak solutions to a non-homogeneous Neumann problem. They also provide some particular cases and an example to illustrate the main results in this paper.

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